Number theory and arithmetic geometry. My areas of study include
modular forms, elliptic curves, partitions, degeneration of
curves and jacobians and K3 surfaces.
Recent Publications
Congruences for l-regular partition functions
modulo 3
(with
David Furcy),
Ramanujan Journal 27 (2012), no. 1, 101-108.
Average Frobenius distributions for elliptic curves
over abelian extensions
(with
Neil Calkin, Bryan Faulkner, Kevin James and Matt King),
Acta Arithmetica 149 (2011), no. 3, 215-244.
l-divisibility of l-regular partition functions
(with
Brian Dandurand),
Ramanujan Journal 19 (2009), no. 1, 63-70.
Arithmetic properties of non-harmonic weak Maass forms
(with Kathrin Bringmann),
Proceedings of the American Mathematical Society 137 (2009), 825-833.
Divisibility properties of the 5-regular and 13-regular partition functions
(with Neil Calkin, Nate Drake, Kevin James, Shirley Law, Philip Lee and Jeanne Radder),
Integers 8 (2008), no. 2, A60, 10pp.
p-adic properties of Maass forms arising from theta series
(with Sharon Garthwaite),
Mathematical Research Letters 15 (2008), no. 3, 459-470.
Arithmetic of l-regular partition functions,
International Journal of Number Theory 4 (2008), no. 2, 295-302.
Education
Ph.D. in Mathematics, University of Georgia, 1998.
M.S. in Physics, University of Michigan, 1991.
B.S. in Physics and Mathematics, University of Wisconsin, 1990.
I am currently in the process of
hiking the Appalachian Trail, section
by section.
So far I have hiked from the trailhead at Springer Mountain in Georgia
to Hanover, New Hampshire,
about 1730 miles. My all-time favorite hike is the
Wonderland Trail,
which I would recommend
highly to anyone who loves hiking, and here are pictures
from two that are not far behind:
the
Four Pass Loop
and the
Teton Crest Trail.
For a flat state Wisconsin offers some excellent mountain biking.
In particular, Kettle Moraine State Park
has the Greenbush trail system
in its
north unit
and the John Muir and Emma Carlin trails
in the
south. If you
are looking for a place to ride
in the Fox Valley,
I would recommend
Brown
County Reforestation Camp.